arXiv subjects

Yaolin Yu

Publications and source records attributed to Yaolin Yu.

3 recordsLinked to original sources

arXiv2026

Continuous stochastic flows driven by white noise and their duals

We study a class of continuous stochastic flows driven by a space-time white noise and characterize their dual flows by explicit stochastic differential equations. A key ingredient of the proof is the convergence of solutions under coefficient approximations. As an application, we derive the dual flows in two illustrative examples, the squared Bessel flow and the Jacobi flow. We also introduce a new model of polynomially self-repelling (PSR) flow and show that it enjoys a self-duality property.

math.PR↗

arXiv2026

The Polynomially Self-repelling Motion

[Kosygina et al. 2023] showed that the rescaled polynomially self-repelling walk does not converge to any Brownian motion perturbed at extrema (BMPE). Motivated by this result, we introduce an explicit candidate for the scaling limit, the polynomially self-repelling motion (PSRM), and study its properties. The construction relies on a new family of continuous stochastic flows, called polynomially self-repelling flows, introduced in [Yu 2026]. A key ingredient in relating the limiting process of the rescaled walk to the PSRM is a joint Ray-Knight theorem for rescaled local time processes, extending the classical Ray-Knight theorems of [Tóth 1996].

math.PR↗

arXiv2024

Meeting of squared Bessel flow lines and application to the skew Brownian motion

We study the meeting level between squared Bessel (BESQ) flow lines of different dimensions, and show that it gives rise to a jump Markov process. We apply these results to the skew Brownian flow introduced by Burdzy and Chen \cite{burdzy2001local} and Burdzy and Kaspi \cite{burdzy2004lenses}. It allows us to extend the results of \cite{burdzy2001local} and of Gloter and Martinez \cite{gloter2013distance} describing the local time flow of skew Brownian motions. Finally, we compute the Hausdorff dimension of exceptional times revealed by Burdzy and Kaspi \cite{burdzy2004lenses} when skew Brownian flow lines bifurcate.

math.PR↗